Hypothesis Testing for the Mean
Known
(z-test)

Given Data | Given Statistics

1. Given this Population Data:

Test the claim that : < 80 for these data using = 0.10:

 60 70 75 55 80 55 50 40 80 70 50 95 120 90 75 85 80 60 110 65 80 85 85 45 75 60 90 90 60 95 110 85 45 90 70 70

Note that is 80.

First enter the data in by pressing STAT and selecting 1:Edit by pressing ENTER. Then run 1-Var Statistics. The result is shown below

Press STAT, then RIGHT ARROW twice to TESTS. Press 1 to select 1:Z-test. If Data is not already highlighted, LEFT ARROW to highlight it, and then press ENTER to select the data mode.

ARROW DOWN once and enter 80 next to :. ARROW DOWN once to :. In order to enter here, press VARS, type 5 to select 5:Statistics, and then type 3 to select 3:. As we ARROW DOWN, will be replaced by the computed value 19.16097224. Make sure the defaults of for List: and 1 for Freq: are also listed.

ARROW DOWN to :. Use the arrow keys to highlight <, since the claim being tested is < 80. Press ENTER. ARROW DOWN to select Calculate, and then press ENTER. The results are shown below.

Conclusions based on z-value:
The test z value shown above is z = -1.59. Using the invNorm function for = 0.10, we find that invNorm(0.10) = -1.28.
This is a left-tailed test, so since -1.59 < -1.28, we are in the rejection region, so reject : 80, and accept the alternative hypothesis :< 80.

Conclusions based on P-value:
The test p value shown above is p = 0.0561553908. The decision is to reject : 80, since 0.0561553908 < 0.10; that is, p < .

2. Given Statistics.

Test the claim : = 8 when = 0.6, = 8.2, and n = 32 using = 0.05. We use : 8

Press STAT, then RIGHT ARROW twice to TESTS. Press 1 to select 1:Z-test. If STATS is not highlighted, ARROW RIGHT once and press ENTER to select STATS.

ARROW DOWN once and enter the value of 8 for . ARROW DOWN once and enter .6 for . ARROW DOWN once more and enter 8.2 for . ARROW DOWN once and enter 36 for n.

Now we must choose which test. Since this is a two-tailed test, ARROW DOWN once to : then use the LEFT or RIGHT ARROW to select , then press ENTER. ARROW DOWN one last time to Calculate and then press ENTER. The results are shown below.

Conclusions based on z-value:
The test z value shown above is z = 1.89. Using the invNorm function for = 0.05 and the fact that this is a two-tailed test, we find that invNorm(0.025) = 1.96. Thus z < -1.96 or z > 1.96 would place our test value in the rejection region. But it is the case that -1.96 < 1.89 < 1.96.
The decision is that we cannot reject : = 8.

Conclusions based on P-value:
The test p value shown about is p = 0.0593463074. Thus, we cannot reject : = 8 since 0.053463074 > 0.05